Let R be a commutative ring with identity, and M be unital (left) R-module. In this paper we introduce and study the concept of small semiprime submodules as a generalization of semiprime submodules. We investigate some basis properties of small semiprime submodules and give some characterizations of them, especially for (finitely generated faithful) multiplication modules.
As an important resource, entanglement light source has been used in developing quantum information technologies, such as quantum key distribution(QKD). There are few experiments implementing entanglement-based deterministic QKD protocols since the security of existing protocols may be compromised in lossy channels. In this work, we report on a loss-tolerant deterministic QKD experiment which follows a modified “Ping-Pong”(PP) protocol. The experiment results demonstrate for the first time that a secure deterministic QKD session can be fulfilled in a channel with an optical loss of 9 dB, based on a telecom-band entangled photon source. This exhibits a conceivable prospect of ultilizing entanglement light source in real-life fiber-based
... Show MoreThe topic of the research revolves around constructivist theory, which is one of the most important theories that added weight to the theoretical and epistemological field of international relations. The constructivist theory studies international relations from a completely different side of theories by focusing on the social aspects of international relations, and by looking at international relations as social constructs. Ideas, cultures, norms, standards and language play a major role in their formation. The study also examines the state of the war on terrorism as it represents one of the most international cases in which its composition and composition coincide with constructive ideas and a
... Show MoreIn this paper mildly-regular topological space was introduced via the concept of mildly g-open sets. Many properties of mildly - regular space are investigated and the interactions between mildly-regular space and certain types of topological spaces are considered. Also the concept of strong mildly-regular space was introduced and a main theorem on this space was proved.
Throughout this work we introduce the notion of Annihilator-closed submodules, and we give some basic properties of this concept. We also introduce a generalization for the Extending modules, namely Annihilator-extending modules. Some fundamental properties are presented as well as we discuss the relation between this concept and some other related concepts.
Let R be a commutative ring with identity and M be a unitary R- module. We shall say that M is a primary multiplication module if every primary submodule of M is a multiplication submodule of M. Some of the properties of this concept will be investigated. The main results of this paper are, for modules M and N, we have M N and HomR (M, N) are primary multiplications R-modules under certain assumptions.
Let R be a ring with identity and M is a unitary left R–module. M is called J–lifting module if for every submodule N of M, there exists a submodule K of N such that
Let R be an associative ring with identity and let M be right R-module M is called μ-semi hollow module if every finitely generated submodule of M is μ-small submodule of M The purpose of this paper is to give some properties of μ-semi hollow module. Also, we gives conditions under, which the direct sum of μ-semi hollow modules is μ-semi hollow. An R-module is said has a projective μ-cover if there exists an epimorphism
Let R be a ring with identity and let M be a left R-module. M is called µ-lifting modulei f for every sub module A of M, There exists a direct summand D of M such that M = D D', for some sub module D' of M such that A≤D and A D'<<µ D'. The aim of this paper is to introduce properties of µ-lifting modules. Especially, we give characterizations of µ-lifting modules. On the other hand, the notion of amply µ-supplemented iis studied as a generalization of amply supplemented modules, we show that if M is amply µ-supplemented such that every µ-supplement sub module of M
... Show MoreThe aim of this work is to give the new types for diskcyclic criterion. We also introduced the case if there is an equivalent relation between a diskcyclic operator and T that satisfies the diskcyclic criterion. Moreover, we discussed the condition that makes T, which satisfies the diskcyclic criterion, a diskcyclic operator
The main goal of this paper is to introduce and study a new concept named d*-supplemented which can be considered as a generalization of W- supplemented modules and d-hollow module. Also, we introduce a d*-supplement submodule. Many relationships of d*-supplemented modules are studied. Especially, we give characterizations of d*-supplemented modules and relationship between this kind of modules and other kind modules for example every d-hollow (d-local) module is d*-supplemented and by an example we show that the converse is not true.